Y=CoE^kt
Co = initial amount
Y= what amount is left
K= rate
T= time
First you have to find the rate
Since in 18.4 days you will have 1/2 left you set it up like this:

1/2Co=CoE^kt
Now the Co's cancel and you're left with :
1/2=e^kt
t=18.4
1/2=e^k(18.4)
Take the natural log of both sides now
ln(.5)=lne x 18.4k
-.6931471806 = 1 x 18.4k
divide by 18.4
k = -.0377
Now you must find the time it takes to go from 50 to 10.
10=50e^kt
k we know = -.0377 and we're looking for t

You should be able to figure it out from here.

(sorry if my work doesn't look fancy, I'm new to this stuff - I'll pick it up eventually)